Welcome to Math 32B! This is only the fourth quarter in the calculus sequence, but it contains the most advanced and interesting calculations in the six quarter series. Essentially the course is devoted to developing integral calculus for functions of two and three variables. This has a range of applications from the geometry of solid bodies to the physics of fluids to probability theory. The Fundamental Theorem of Calculus has generalizations to higher dimensions, the theorems of Green, Stokes and Gauss, which are the basis for studying electricity and magnetism. The syllabus for the course consists of just two chapters in Stewart: Chapter 16 which sets up definite integrals in two and three dimensions, and Chapter 17 which deals with the generalizations of the Fundamental Theorem. However, there is plenty here for a full and, I hope, interesting quarter.

Office Hours: J. Ralston, MS5238 Mon 2-3,Tues 10-11,2-3, Wed 9-10,Thurs. 10-11.

C-Y. Kao, MS3905, Tues. 1-2, Thurs. 11-12.

D. Weisbart, MS2341, Tues 12-1, Thurs 3-4(tentative). Also Tues 11-12 in the student math center.

Homework: The exercises listed below are to written up and handed in on Fridays (in two cases Mondays) in class according to the following schedule:

Assignments from Sept. 29, Oct. 2, Oct. 4 and Oct. 6 are due Oct. 9.

Assignments from Oct. 9, 0ct. 11 and Oct. 13 are due Oct. 20.

Assignments from Oct. 16, Oct. 18, and Oct. 20 are due Oct. 27.

Assignments from Oct. 27 and Oct. 30 are due Nov. 3.

Assignments from Nov. 1, Nov. 3 and Nov. 6 are due Nov. 13.

Assignments from Nov. 8 and Nov. 13 are due Nov. 20.

Assignments from Nov. 20, Nov. 22 and Nov. 27 are due Dec. 1.

Assignments from Nov. 29, Dec. 1 and Dec. 4 are due Friday,Dec. 8.

Homework will be corrected and handed back in your weekly quiz sections. Late homework will not be accepted. The assignments are not very long because our readers can only be paid for a limited amount of grading. Many of the topics in this course require more practice. Fortunately Stewart, like all calculus books, has a great many additional problems like those assigned, and the answers to the odd-numbered ones are in the back of the book. Please take advantage of this for further practice.

Grading: Your grade in this course will be computed from your grades on the homework, hour exams and final exam with the following weights 20% on the homework, 20% on each hour exam, and 40% on the final. The Final Examination is cumulative, i.e. it covers the entire syllabus. What will be covered on the hour exams will be announced beforehand in class. Whatever happens, the dates of the hour exams will not change, and they will be given only on those dates.

SYLLABUS AND EXERCISES

Sept. 29 Section 16.1 Double Integrals over Rectangles. Exercises: 7,12,13,17.

Week 1

Oct. 2 Section 16.2 Iterated Integrals. Exercises: 8,9,18,23.

Oct. 4 Section 16.3 Double Integrals over General Regions. Exercises: 11,14,27,35,38. Also see if you can guess the answers to 17,45 and 51 from symmetry.

Oct. 6 Section 16.4 Double Integrals in Polar Coordinates. Exercises: 8,11,18,23.

Week 2

Oct. 9 Section 16.5 Applications of Double Integrals. Exercises: 4,11,25,26.

Oct.11 Section 16.6 Surface Area. Exercises: 3,6,11,22.

Oct.13 Section 16.7 Triple Integrals. Exercises: 7,13,18,29.

Week 3

Oct.16 Section 16.8 Triple Integrals in Special Coordinates. Exercises: 4,7,18,33,35.

Oct.18 Section 16.9 Change of Variables in Multiple Integrals. Exercises: 2,3,7,10.

Oct.20 Section 16.9 continued. Exercises: 11,14,15,22,24.

Week 4

Oct.23 Review

Oct.25 Hour Exam I

Oct.27 Section 17.1 Vector Fields. Exercises: 3,11-14,24,29-32.

Week 5

Oct. 30 Section 17.2 Line Integrals. Exercises: 3,7,19,24.31.

Nov. 1 Section 17.3 The Fundamental Theorem for Line Integrals. Exercises: 2,3,4,7,11,14.

Nov. 3 Section 17.4 Green's Theorem. Exercises: 2,7,10,13,15.

Week 6

Nov. 6 Section 17.4 continued. Exercises: 19,21,22,29.

Nov. 8 Section 17.5 Curl and Divergence. Exercises: 5,7,12,15,17,19,26.

Nov.10 Veteran's Day Holiday

Week 7

Nov.13 Section 17.6 Parametric Surfaces and Their Areas. Exercises: 1-4,11-16,17,30,33.

Nov.15 Review

Nov.17 Hour Exam II. This will cover sections 16.9 and 17.1-4. Some review problems: 49 and 51 from the review problems for Chpt. 16, 1.a, 2,3,4 (Answer: 3/2), 5 (Use Green!),7,9,11,13 and 17 from the review problems for Chpt. 17. Also, from the individual sections: Sect. 17.2: 33.b, 37, Sect. 17.3: 15,17,19, and Sect. 17.4: 3,9,17.

Week 8

Nov.20 Section 17.7 Surface Integrals. Exercises: 4,5,7,10,13.

Nov 22 Section 17.7 continued. Exercises: 23,28,35,39,41.

Nov.24 Thanksgiving Day Holiday

Week 9

Nov.27 Section 17.8 Stokes' Theorem. Exercises: 4,7,9,10.

Nov.29 Section 17.8 continued. Exercises: 13,18,19,20.

Dec.1 Section 17.9 The Divergence Theorem. Exercises: 4,6,9,13,19.

Week 10

Dec. 4 Section 17.9 continued. Exercises: 19,20,24,29,30.

Dec. 6 Review

Dec. 8 Review

FINAL EXAMINATION, Wednesday, December 13, 11:30-2:30

The final will be given in FRANZ HALL 1178